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http://functions.wolfram.com/07.31.04.0003.02
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HypergeometricPFQ[{Conjugate[Subscript[a, 1]], \[Ellipsis],
Conjugate[Subscript[a, p]]}, {Conjugate[Subscript[b, 1]], \[Ellipsis],
Conjugate[Subscript[b, q]]}, Conjugate[z]] ==
Conjugate[HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis],
Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]},
z]] /; !(IntervalMemberQ[Interval[{1, Infinity}], z] && p == q + 1)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["Conjugate", "[", SubscriptBox["a", "1"], "]"]], ",", "\[Ellipsis]", ",", RowBox[List["Conjugate", "[", SubscriptBox["a", "p"], "]"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["Conjugate", "[", SubscriptBox["b", "1"], "]"]], ",", "\[Ellipsis]", ",", RowBox[List["Conjugate", "[", SubscriptBox["b", "q"], "]"]]]], "}"]], ",", RowBox[List["Conjugate", "[", "z", "]"]]]], "]"]], "\[Equal]", RowBox[List["Conjugate", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]], "]"]]]], "/;", RowBox[List["Not", "[", RowBox[List[RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", "z"]], "]"]], "\[And]", RowBox[List["p", "\[Equal]", RowBox[List["q", "+", "1"]]]]]], "]"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mi> p </mi> </msub> <msub> <mi> F </mi> <mi> q </mi> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mover> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> _ </mo> </mover> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mover> <msub> <mi> a </mi> <mi> p </mi> </msub> <mo> _ </mo> </mover> </mrow> <mo> ; </mo> <mrow> <mover> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> _ </mo> </mover> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mover> <msub> <mi> b </mi> <mi> q </mi> </msub> <mo> _ </mo> </mover> </mrow> <mo> ; </mo> <mover> <mi> z </mi> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[TagBox[OverscriptBox[SubscriptBox["a", "1"], "_"], HypergeometricPFQ, Rule[Editable, True]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[TagBox[OverscriptBox[SubscriptBox["a", "p"], "_"], HypergeometricPFQ, Rule[Editable, True]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[TagBox[OverscriptBox[SubscriptBox["b", "1"], "_"], HypergeometricPFQ, Rule[Editable, True]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[TagBox[OverscriptBox[SubscriptBox["b", "q"], "_"], HypergeometricPFQ, Rule[Editable, True]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[OverscriptBox["z", "_"], HypergeometricPFQ, Rule[Editable, True]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> <mo> ⩵ </mo> <mover> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mi> p </mi> </msub> <msub> <mi> F </mi> <mi> q </mi> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> <mo> ; </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> <mo> _ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mo> ¬ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ∈ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mi> p </mi> <mo> ⩵ </mo> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mi> p </mi> </msub> <msub> <mi> F </mi> <mi> q </mi> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mover> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> _ </mo> </mover> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mover> <msub> <mi> a </mi> <mi> p </mi> </msub> <mo> _ </mo> </mover> </mrow> <mo> ; </mo> <mrow> <mover> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> _ </mo> </mover> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mover> <msub> <mi> b </mi> <mi> q </mi> </msub> <mo> _ </mo> </mover> </mrow> <mo> ; </mo> <mover> <mi> z </mi> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[TagBox[OverscriptBox[SubscriptBox["a", "1"], "_"], HypergeometricPFQ, Rule[Editable, True]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[TagBox[OverscriptBox[SubscriptBox["a", "p"], "_"], HypergeometricPFQ, Rule[Editable, True]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[TagBox[OverscriptBox[SubscriptBox["b", "1"], "_"], HypergeometricPFQ, Rule[Editable, True]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[TagBox[OverscriptBox[SubscriptBox["b", "q"], "_"], HypergeometricPFQ, Rule[Editable, True]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[OverscriptBox["z", "_"], HypergeometricPFQ, Rule[Editable, True]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> <mo> ⩵ </mo> <mover> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mi> p </mi> </msub> <msub> <mi> F </mi> <mi> q </mi> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> <mo> ; </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> <mo> _ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mo> ¬ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ∈ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mi> p </mi> <mo> ⩵ </mo> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1},z] | HypergeometricPFQ[{a1,a2},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] | |
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